Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 301 / 1 / iii

Scale invariance requires the potential to obeyThus, apart from the zero choice,for a dimensionless constant $g$; an additive constant is excluded because it introduces a scale in the action. The canonical dilatation current isUsing $\square \varphi +V^{\prime }(\varphi )=0$,Equivalently, after improving the stress tensor to make it traceless, the current is $x_{\nu }{T}_{\mathrm{imp}}^{\mu \nu }$.